Tag - String theory

Rajesh Gopkumar: Deriving Gauge-String Duality

1st February, 2022

Gauge (or Yang-Mills) theories are the building blocks of our current physical understanding of the universe. In parallel, string theory is a framework for a consistent quantum description of gravity. Gauge-String duality a.k.a. the AdS/CFT correspondence is a remarkable connection between these two very different classes of theories. This has, in fact, been one of the main engines driving progress in theoretical physics over the last two decades. I will begin by discussing why it is important to arrive at a first principles understanding of the underlying mechanism of this duality relating quantum field theories and string theories (or other theories of gravity). I will then proceed to discuss a very general approach which aims to relate large N QFTs and string theories, starting from free field theories. This corresponds to a tensionless limit of the dual string theory on AdS spacetime. Finally, I will discuss specific cases of this limit for AdS3/CFT2 and AdS5/CFT4, where one has begun to carry this programme through to fruition, going from the string theory to the field theory and vice versa.

Hülya Argüz: Enumerative geometry and mirror symmetry for log Calabi-Yau pairs

23rd September, 2021

Given a log Calabi-Yau pair (X,D), consisting of a smooth projective variety X together with a normal crossings anti-canonical divisor D, we first provide a combinatorial algorithm for solving the enumerative problem of computing rational stable maps to (X,D) touching D at a single point. We then explain how to use the solution to write explicit equations for mirrors to such pairs at
arbitrary dimensions.

Ralph Kaufmann: Feynman categories, universal operations and master equations

6th December, 2013

Feynman categories are a new universal categorical framework for generalizing operads, modular operads and twisted modular operads. The latter two appear prominently in Gromov-Witten theory and in string field theory respectively. Feynman categories can also handle new structures which come from different versions of moduli spaces with different markings or decorations, e.g., open/closed versions or those appearing in homological mirror symmetry. For any such Feynman category there is an associated Feynman category of universal operations. These give rise to Gerstenhaber's famous bracket, the pre-Lie structure of string topology, as well as to the Lie bracket underlying the three geometries of Kontsevich built from symplectic vector spaces. As time permits, we will also briefly discuss bar, co-bar and Feynman transforms and how these give rise to master equations, such as the Maurer-Cartan equation or the BV master equation.